Evidence for ferroaxial order in 1T-TiSe$_2$ via elastoresistivity measurements
The study of spontaneous symmetry breaking and electronic order is fundamental in condensed matter physics. Hidden order, symmetry-breaking states that elude conventional probes, potentially plays a crucial role in understanding complex quantum phases in a wide range of materials. Ferroaxial order, a state characterized by broken mirror symmetries while maintaining time-reversal and inversion symmetries, is one of the hidden orders that have proven most challenging to detect experimentally. Here, we demonstrate a new approach for investigating both the ferroaxial order parameter and ferroaxial susceptibility using elastoresistivity measurements. We do this for 1T-TiSe$_{2}$, a material that exhibits charge density wave order that has eluded comprehensive understanding for a long time. These measurements reveal an anomalous off-diagonal linear elastoresistivity in the CDW state. We discuss why this provides a smoking gun for ferroaxial order. Furthermore, we construct an appropriate combination of the symmetry-breaking strains $\epsilon_{x^2-y^2}$ and $\epsilon_{xy}$ that acts as an effective conjugate field for the ferroaxial order, and demonstrate how sweeping this effective field in the CDW state results in a hysteretic behavior of the elastoresistivity, associated with the movement of ferroaxial domain walls. Finally, we reveal a divergence of certain nonlinear elastoresistivity coefficients above the critical temperature, and discuss how this is consistent with a divergence of the ferroaxial susceptibility near T$_{\rm{CDW}}$ $\sim$ 200K. Our study also includes detailed elastocaloric measurements, which reveal the presence of an additional phase transition several tens of Kelvin below T$_{\rm{CDW}}$. Our results provide new insight into the symmetry of the ordered state in 1T-TiSe$_2$ and establish elastoresistivity as a powerful probe of hidden order and its symmetry.